Abstract

If P$_{N}$(nl; r) is the (nl) wave function for an electron in an atom of atomic number N, and P$_{\text{H}}$(nl; r) is the corresponding hydrogen wave function, then, for a given configuration and large N N$^{-\frac{1}{2}}$P$_{N}$(nl; r) = P$_{\text{H}}$(nl; Nr) + (1/N) Q(nl; Nr) + (1/N$^{2}$) R(nl; Nr) + O(1/N$^{3}$). The equations for the functions R(nl; Nr) have been set up and solved for the configurations whose outer groups are (2p)$^{6}$, (3s)$^{2}$, (3p)$^{6}$, (3d)$^{5}$ and (3d)$^{10}$. From the solutions the limiting slope of a screening number $\sigma $(nl) as a function of the mean radius $\overline{r}$ has been computed for $\overline{r}$ = 0. It was found that the variation with respect to $\overline{r}$ of $\sigma $(3s) and $\sigma $(3p) of the (3d)$^{10}$ configuration was far from linear. Plots of $\sigma $(nl) as functions of $\overline{r}$ have been drawn more accurately than was possible previously. As a result the estimation of wave functions using a process of interpolation will be more accurate as well.